The socket in that is a PGA478. In theory, that CPU might be changeable. Maybe.
But not to an i5 of any sort.
https://www.cnet.com/reviews/gateway-one-zx4800-review/
https://ark.intel.com/products/37253/Intel-Pentium-Processor-T4300-1M-Cache-2-10-GHz-800-MHz-FSB-
There are a limited number of CPU's that might fit that socket, and none of them a real increase over what you currently have.
http://www.tomsguide.com/forum/58474-35-fastest
And then you get into the BIOS and power requirements.
Will the current BIOS accept a different CPU? Maybe, maybe not.
All In One's are basically laptops in a different configuration. Not really user upgradeable.
That system is a decade old (2009). It's had a good run.